Related papers: Algebrodynamical Approach in Field Theory: Bisingu…

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…

Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…

The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…

Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…

This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter's theory of regular, quaternionic functions. The algebras of quaternions…

We call attention to the unusual properties that the 4 dimensional solutions for a modified Fueter-Dirac equations satisfy: In a coordinate-free, constant-free and strictly mathematical way it is possible to show that all the solutions for…

Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of…

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…

This paper exposes a reformulation of some gauge theories in terms of explicitly gauge-invariant variables. We show in the case of Scalar QED that the classical theory can be reformulated locally with some gauge invariant variables. We…

We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…

We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…

A scalar field can be inserted in Maxwell and/or Einstein theory to effect symmetry breaking. Consequences of such a modification are discussed. Possible dynamics for the scalar field are presented.

Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…

The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…

We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other…

The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…

The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…

In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary base fields is presented, as well as quadratic form theoretic…

By means of an appropriate re-scaling of the metric in a Lagrangian, we are able to reduce it to a kinetic term only. This form enables us to examine the extended complexified solution set (complex moduli space) of field theories by finding…